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Moutard Transform for Generalized Analytic Functions

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Abstract

We construct a Moutard-type transform for generalized analytic functions. The first theorems and the first explicit examples in this connection are given.

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Acknowledgments

The main part of the work was fulfilled during the visit of the first author to the Centre de Mathématiques Appliquées of École Polytechnique in October 2015. The first author was partially supported by the Russian Foundation for Basic Research, Grant 13-01-12469 ofi-m2, by the Program “Leading scientific schools” (Grant NSh-4833.2014.1), by the Program “Fundamental problems of nonlinear dynamics”.

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Authors and Affiliations

  1. L.D. Landau Institute for Theoretical Physics, pr. Akademika Semenova 1a, Chernogolovka, Russia, 142432

    P. G. Grinevich

  2. Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, GSP-1, Leninskiye Gory 1, Main Building, Moscow, Russia, 119991

    P. G. Grinevich

  3. Moscow Institute of Physics and Technology, 9 Institutskiy per., Dolgoprudny, Moscow Region, Russia, 141700

    P. G. Grinevich

  4. CNRS (UMR 7641), Centre de Mathématiques Appliquées, École Polytechnique, 91128, Palaiseau, France

    R. G. Novikov

  5. IEPT RAS, Moscow, Russia, 117997

    R. G. Novikov

Authors
  1. P. G. Grinevich
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  2. R. G. Novikov
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Correspondence to R. G. Novikov.

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Grinevich, P.G., Novikov, R.G. Moutard Transform for Generalized Analytic Functions. J Geom Anal 26, 2984–2995 (2016). https://doi.org/10.1007/s12220-015-9657-8

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  • DOI: https://doi.org/10.1007/s12220-015-9657-8

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